Problem: Multiply the following complex numbers, marked as blue dots on the graph: $(2 e^{7\pi i / 6}) \cdot (4)$ (Your current answer will be plotted in orange.)
Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $2 e^{7\pi i / 6}$ ) has angle $\frac{7}{6}\pi$ and radius $2$ The second number ( $4$ ) has angle $0$ and radius $4$ The radius of the result will be $2 \cdot 4$ , which is $8$ The angle of the result is $\frac{7}{6}\pi + 0 = \frac{7}{6}\pi$ The radius of the result is $8$ and the angle of the result is $\frac{7}{6}\pi$.